I have always grown the following neps in water trays and never had a problem with any
Veillardii (but not in winter as it likes it drier)
maxima X alata
camp X vent
truncate X maxima
gothica (which also makes deformed lids and small 3-4inch traps and has high light and humidity)
a couple others, but you get the gist
Plants that hated trays and don't get them are truncate, veitchii, pervillei and dyreana.
Most of my neps are in my greenhouse (shade cloth, misters), others are just in hanging pots in tree's watered by rain and a few are in my polyhouse here at uni.
I am also in tropical north QLD, so as I don't get many cold persistent temp swings rot has never been a real issue (except for crown rot but the tray would not cause this).